Perfect sampling from the limit of deterministic products of stochastic matrices. (English) Zbl 1188.15029

Stenflo, Örjan

Electron. Commun. Probab. 13, 474-481 (2008).

Summary: We illustrate how a technique from the theory of random iterations of functions can be used within the theory of products of matrices. Using this technique we give a simple proof of a basic theorem about the asymptotic behavior of (deterministic) “backwards products” of row-stochastic matrices and present an algorithm for perfect sampling from the limiting common row-vector (interpreted as a probability-distribution).

MSC:

15B51	Stochastic matrices
65C05	Monte Carlo methods
60J10	Markov chains (discrete-time Markov processes on discrete state spaces)
65C40	Numerical analysis or methods applied to Markov chains

Keywords:

perfect sampling; stochastic matrices; Markov chain Monte Carlo; iterated function systems; products of matrices; algorithm